Observation and Modeling of a Sharp Oxygen Threshold in Aqueous Free Radical and RAFT Polymerization

It is known that oxygen (O2) stops radical polymerization (RP). Here, it was found that the reaction turn-off occurs abruptly at a threshold concentration of O2, [O2]t, for both free RP and reversible addition–fragmentation chain-transfer polymerization (RAFT). In some reactions, there was a spontaneous re-start of conversion. Three cases were investigated: RP of (i) acrylamide (Am) and (ii) sodium styrene sulfonate (SS) and (iii) Am RAFT polymerization. A controlled flow of O2 into the reactor was employed. An abrupt turn-off was observed in all cases, where polymerization stops sharply at [O2]t and remains stopped when [O2] > [O2]t. In (i), Am acts as a catalytic radical-transfer agent during conversion plateau, eliminating excess [O2], and polymerization spontaneously resumes at [O2]t. In no reaction, the initiator alone was capable of eliminating O2. N2 purge was needed to re-start reactions (ii) and (iii). For (i) and (ii), while [O2] < [O2]t, O2 acts a chain termination agent, reducing the molecular weight (Mw) and reduced viscosity (RV). O2 acts as an inhibitor for [O2] > [O2]t in all cases. The radical-transfer rates from Am* and SS* to O2 are >10,000× higher than the initial chain propagation step rates for Am and SS, which causes [O2]t at very low [O2].


S1.2. Reaction Monitoring
ACOMP concentrations of Am and SS were calculated using the 250 and 260 nm raw UV signals, respectively. The reactor content stream was conditioned through two consecutive dilution stages, providing dilutions ranging from 20 to 81x, for the Am RP reactions, and from 10 to 18x for Am RAFT reactions. Given the strong UV absorption of the SS molecule, for the SS RP reactions, the dilution of the content stream going into the UV was increased substantially, to over 400x. Overall, total solids content (monomer + polymer) going through the UV ranged between 0.065x10 -3 and 2.76x10 -3 g/cm 3 , while staying between 1.05x10 -3 and 4.85x10 -3 g/cm 3 , for the other two detectors during RP and RAFT, respectively. Temperature and stirring were appropriately controlled, using a magnetic stirrer at the highest possible speed (RPM) setting -1000 RPMto ensure better mixing of the O2 in the reactor content. Figure SI1 below provides a simplified illustration of the set up used for all reactions, including both ACOMP and RDO probe monitoring. Figure S1. Experimental setup employed showing monitoring by online technique ACOMP and in situ RDO probe. Also shown are some of the parameters automatically calculated on the ACOMP proprietary software. PE = extraction pump, GFM = gas flow meter/controller, T = stir + heat plate temperature probe. Details on the dilution stages used on the ACOMP system were omitted for simplification.

S1.3. Offline GPC Analyses
Deionized water was used as the mobile phase for the GPC system, which consisted of a Rheodyne 7725i manual injector, with a 100μL sample loop, connected to a Shimadzu LC-10AT VP pump, and a Shimadzu SPD-10AV UV detector with a 1 cm flow cell, followed by a Shimadzu RID-10A refractive index detector. A Shodex OHpak SB-802.5 HW column was chosen for all analyses of the reaction aliquots, as it is able to separate monomer and low molar mass polymers, allowing to track any intermediate shorter polymer chains formed, which further confirms that no polymerization happened during the conversion plateau. The GPC data were custom analyzed. To test Equations 1 and 2 (main manuscript), two analogous set of experiments with a compressed air flow rate of 75 sccm were carried outone with 350 ml/250 ml headspace/water and one with 100 ml/500 ml headspace/water volumes ( Figure SI2).   Figure SI4 shows the differences in rate between O2 concentration in the solution and in headspace during RP reactions carried out under the same conditions -identical compressed air flow periods (1800 s, or 30 min) at 200 sccm, reactions 9A and 10A in Table 1, respectively). Although the headspace concentration data are just qualitative -O2 concentration measurements are accurate only in solutionthe O2 rise value,  in Equation 1 (main manuscript), can be accurately determined and is very much different and, in accordance with Table 2 (main manuscript), the amount of O2 in the headspace is significantly higher than in solution. Although the calculated value for [O2]plateau in solution is 50% higher than that of the headspace, the fit only reaches the plateau after 50000 s, which is much longer than the 5000 s it would take to reach the observed values around 6 mg/L, from the control experiments. The same trend can be seen during the initial O2 purge with N2 at 75 sccm (time < 0) -[O2] in headspace drops dramatically right away since the headspace fills up quicker with N2, as opposed to a much smoother reduction in solution. The table in Figure SI4 shows the calculated values from the 1 st order fitting of the data for  fall and  rise -[O 2 ] decrease rate during purge with N 2 and increase rate during compressed air flow period, respectively. Again, the values obtained for the headspace are at least one order of magnitude higher than those for the solution monitoring.  Table 1, respectively). The diamonds in each curve mark the beginning and the end of compressed air flow period. The concentration in the headspace is relative, but  can be accurately determined. Figure S5. Cumulative weight average molecular weight (Mw) for polymerization of Am with 6 sccm airflow and with no O2 (reactions 12A and 13A in Table 1, respectively).

S8
The time-dependent signatures of [O2] in the reactor allow for some modeling of the process, provide further evidence of the reactions in the above kinetic model, and an estimate of the total amount of O2 consumed during the air flow, and after it is stopped. The following derivation is based on these two assumptions: 1) the reactor is vented to atmosphere via a needle, so it is assumed that the headspace of the reactor remains at atmospheric pressure throughout. Because the needle is small-bore this assumption may not be strictly true, and there could be some small, transient pressure increases in the headspace as air flows into the reactor. 2) the volume of liquid in the reactor over the conversion plateau does not change significantly. It was found experimentally that the mixing of inflowing O2 into the headspace and dissolution into the reactor water, initially N2 purged, does not occur at the same rate (see Figure SI4 above). Consider the case of instantaneous, ideal mixing of O2 flowing with a molar flow rate Q (mol/s) into a vented vessel of volume V originally filled with N2 at atmospheric pressure. Then . In particular, dissolution of the O2 into water yields R about 6.5x lower than H in the headspace, at a 500ml/100ml solution/headspace volume ratio. This difference in rates means that [O2] in the headspace will more quickly get closer to its saturation value than [O2] in the liquid, allowing the headspace O2 to act as a source term of O2 flowing into the liquid, as long as [O2,R]<[O2,R]sat, where [O2,R]sat is the saturation for dissolved O2 in the reactor liquid. This is clearly seen in Figure 3, where the backflow from headspace to liquid was measured directly after airflow was stopped, when no reaction was occurring. In Figure 6 the effect is dramatic during the RAFT reaction, where the [O2,R] increased strongly, well after the airflow stopped due to backflow from headspace to liquid and the suppression of the catalytic O2 elimination cycle observed in RAFT. Even in the RP case (i), such as in Figure 2, there was usually a short period of a small O2 increase after the airflow stopped, due to the headspace backflow, but this was quickly overwhelmed in the RPs by the O2 elimination cycle, causing [O2,R] to decrease after reaching a maximum. Because [O2,H]sat = 58[O2,R]sat, at 50 o C, even a relatively small headspace (VH~100cm 3 versus VR = 500cm 3 ) holds ample O2 for backflow into the reactor.
The effect of the headspace backflow of O2 into the reactor can be expressed with an experimental rate constant  which is related to the diffusivity of O2 from the headspace and dissolution into the reactor liquid, and the amount of interfacial area separating the liquid from the headspace. This leads to a gain of O2 in the reaction given by  The kinetic model predicts that when the Am RP reaction occurs, O2 flowing into the reactor is swept into the process, both in the O2 elimination catalyzed by Am* in case (i), and as an inhibitory chain termination agent below [O2]t in cases (i) and (ii). Hence, in case (i), the rate of increase of [O2] () in the reactor liquid during a polymerization reaction should be less than when O2 flows into a non-reacting aqueous mixture, since [O2] is chemically eliminated during the reaction, but not during a flow into non-reacting aqueous phase.
This prediction for case (i) is born out clearly in Figure 3, where the initial build-up rate of O2 in the reaction, [O2,R], is about 13x slower than when O2 flows at the same rate into nonreacting aqueous reactor content; i.e. the effect of O2 elimination during the reaction is very strong. From Equation 9, O2 in the reactor is chemically eliminated at a rate given by where ′ is the rate when the reaction occurs, and ′ < , since dissolved O2 is being eliminated in the reaction liquid and reduces the flow rate of O2 to the headspace. The two equations are coupled and so are most easily solved numerically. For a quick analytical estimate, however, it can be approximated that, because [O2,H] When the airflow is cut off at tf the new solution, [O2,R]II(t) is again first order, and must match the first solution at t = tf, that is  Figure 3 shows that lim →∞ [ 2, ] ( ) is near the lower limit of sensitivity of the O2 probe, so that c>>, for the reaction conditions determining c and reactor geometry partially determining .
The total amount of O2 eliminated chemically can be estimated for a fixed air flow rate by subtracting from the total amount of O2 at saturation with no reaction the amount of [O2,R] measured at an equivalent time during an RP. This difference is approximately the amount of O2 chemically eliminated over the period. Once the air flow stops, the remaining dissolved O2 will be driven down to the O2 reaction turn-off threshold, [O2,R]t by the reaction, and even lower.
Another way of quickly estimating the catalytic efficiency in case (i) is to consider the number of free radicals generated over 16,000 s from KPS decay, at 50 o C, which equals to only 8.7x10 -8 mol/cm 3 of KPS radicals. Since the amount of O2 eliminated over 16,000 s is ~ 1.14x10 -6 mol/cm 3 , a single I* must suffice to eliminate at least 13 molecules of O2. As proved by the control experiments (see Figures SI3 and 3), this elimination is mediated by Am at this low initiator concentration, so each Am must be able to go through at least 13 catalytic cycles, and likely more, before being used up in a side reaction (e.g. termination).
The prediction from the approximation obtained by eliminating [O2,H] from the balance equation for [O2,R](t) is that it will have a first order growth while the air flow is on, and will subsequently decay to a small but finite value when the airflow stops. This is qualitatively the trends seen for [O2,R](t) during RP. If this approximation is dropped and the coupled equations integrated numerically (not shown), including the changing reactor liquid volume due to ACOMP extraction, the rounding of the decay profile with an inflection point, appears.
As regards shape, at first sight the O2 behavior in Figure 3 appears fairly symmetric. Upon closer inspection and examining many such O2 profiles suggests that the buildup to the maximum is first order, as in pure water, albeit at a much lower rate, and that the downside is initially Gaussian, before becoming exponential. While there were problems with mixing and homogeneity of O2 as far as obtaining accurate O2 data is concerned, the data from numerous experiments allow fair estimates of O2 threshold values, and other features, such as shape, rise time, and peak values.